Plasmonic surface-scattering elements and metasurfaces for optical beam steering

ABSTRACT

Systems and methods are described herein for an optical beam-steering device that includes an optical transmitter and/or receiver to transmit and/or receive optical radiation from an optically reflective surface. An array of adjustable plasmonic resonant waveguides is arranged on the surface with inter-element spacings less than an optical operating wavelength. A controller applies a pattern of voltage differentials to the adjustable plasmonic resonant waveguides. The pattern of voltage differentials corresponds to a sub-wavelength reflection phase pattern for reflecting the optical electromagnetic radiation. One embodiment of an adjustable plasmonic resonant waveguide includes first and second metal rails extending from the surface. The metal rails are spaced from one another to form a channel therebetween. An electrically-adjustable dielectric is disposed within the channel.

If an Application Data Sheet (ADS) has been filed on the filing date ofthis application, it is incorporated by reference herein. Anyapplications claimed on the ADS for priority under 35 U.S.C. §§ 119,120, 121, or 365(c), and any and all parent, grandparent,great-grandparent, etc., applications of such applications are alsoincorporated by reference, including any priority claims made in thoseapplications and any material incorporated by reference, to the extentsuch subject matter is not inconsistent herewith.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of the earliest availableeffective filing date(s) from the following listed application(s) (the“Priority Applications”), if any, listed below (e.g., claims earliestavailable priority dates for other than provisional patent applicationsor claims benefits under 35 U.S.C. § 119(e) for provisional patentapplications, and for any and all parent, grandparent,great-grandparent, etc., applications of the Priority Application(s)).In addition, the present application is related to the “RelatedApplications,” if any, listed below.

Priority Applications

This Application is a continuation application of and claims priority toU.S. patent application Ser. No. 16/659,286, filed on Oct. 21, 2019,titled “Plasmonic Surface-Scattering Elements and metasurfaces forOptical Beam Steering,” scheduled to grant as U.S. Pat. No. 10,627,571on Apr. 21, 2020, which is a divisional application of and claimspriority to U.S. patent application Ser. No. 15/924,744, filed on Mar.19, 2018, also titled “Plasmonic Surface-Scattering Elements andMetasurfaces for Optical Beam Steering,” granted as U.S. Pat. No.10,451,800 on Oct. 22, 2019. Each of the above-identified patentapplications is hereby incorporated by reference in its entirety.

Related Applications

If the listings of applications provided above are inconsistent with thelistings provided via an ADS, it is the intent of the Applicant to claimpriority to each application that appears in the Priority Applicationssection of the ADS and to each application that appears in the PriorityApplications section of this application.

All subject matter of the Priority Applications and the RelatedApplications and of any and all parent, grandparent, great-grandparent,etc., applications of the Priority Applications and the RelatedApplications, including any priority claims, is incorporated herein byreference to the extent such subject matter is not inconsistentherewith.

TECHNICAL FIELD

This disclosure relates to reconfigurable antenna technology.Specifically, this disclosure relates to reconfigurable reflective-typeantenna elements operable at optical frequencies.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates a simplified embodiment of an optical surfacescattering antenna device with adjustable plasmonic resonant waveguides.

FIG. 1B illustrates an example of a single adjustable plasmonic resonantwaveguide extending from a surface with an insulator and reflector.

FIG. 1C illustrates conceptual representations of the electric andmagnetic energy densities within the adjustable plasmonic resonantwaveguide of FIG. 1B with optical excitation at approximately 70°relative to normal with transverse magnetic (TM) polarization.

FIG. 2A illustrates a simplified embodiment of an optical surfacescattering antenna device with reflector patches beneath each of theadjustable plasmonic resonant waveguides.

FIG. 2B illustrates an example of a single adjustable plasmonic resonantwaveguide extending from a surface with an insulator and embeddedreflector patches.

FIG. 2C illustrates conceptual representations of the electric andmagnetic energy densities within the adjustable plasmonic resonantwaveguide of FIG. 2B.

FIG. 3A illustrates a simplified embodiment of an optical surfacescattering antenna device with a notched reflector beneath each of theadjustable plasmonic resonant waveguides.

FIG. 3B illustrates an example of a single adjustable plasmonic resonantwaveguide extending from a surface with an insulator and a notchedreflector.

FIG. 3C illustrates conceptual representations of the electric andmagnetic energy densities within the adjustable plasmonic resonantwaveguide of FIG. 3B.

FIG. 4A illustrates a simplified embodiment of an optical surfacescattering antenna device with an underlying Bragg reflector.

FIG. 4B illustrates an example of a single adjustable plasmonic resonantwaveguide extending from a Bragg reflector surface.

FIG. 4C illustrates conceptual representations of the electric andmagnetic energy densities within the adjustable plasmonic resonantwaveguide of FIG. 4B.

FIG. 5A illustrates a simplified embodiment of an optical surfacescattering antenna device with multi-channel width reflector patchesbeneath each of the adjustable plasmonic resonant waveguides.

FIG. 5B illustrates an example of single adjustable plasmonic resonantwaveguide extending from a surface with an insulator and embeddedmulti-channel width reflector patches.

FIG. 6 illustrates an approximation of the reflection phase of oneexample of a single adjustable plasmonic resonant waveguide as afunction of the refractive index of the electrically-adjustabledielectric.

FIG. 7 illustrates an approximation of the reflection spectrum of oneexample of a high-Q adjustable plasmonic resonant waveguide.

FIG. 8 illustrates a simplified diagram of a steerable beam of reflectedoptical radiation possible via an optical surface scattering antennasimilar to the antenna illustrated in FIG. 1A.

FIG. 9 illustrates a holographic metasurface, control logic, memory, andan input/output port to form a transmit and/or receive optical surfacescattering antenna system.

FIG. 10 illustrates an example of an adjustable plasmonic resonantwaveguide with example dimensions for a particular operationalbandwidth.

FIG. 11A illustrates an example of a tunable optical surface scatteringantenna device with an optical transmitter or receiver.

FIG. 11B illustrates the transmitter (or receiver) transmitting (orreceiving) optical radiation via a steerable optical beam from thetunable optical surface that includes adjustable plasmonic resonantwaveguides.

FIG. 12 illustrates an example embodiment of a packaged solid-statesteerable optical beam antenna system with an optically transparentwindow.

DETAILED DESCRIPTION

In various embodiments, reconfigurable antennas leverage metamaterialsurface antenna technology (MSAT). Metamaterial surface antennas, alsoknown as surface scattering antennas and metasurface antennas, aredescribed, for example, in U.S. Patent Publication No. 2012/0194399,which publication is hereby incorporated by reference in its entirety.Additional elements, applications, and features of surface scatteringantennas that feature a reference wave or feed wave are described inU.S. Patent Publication Nos. 2014/0266946, 2015/0318618, 2015/0318620,2015/0380828 and 2015/0372389, each of which is hereby incorporated byreference in its entirety. Examples of related systems that utilize afree-space reference or feed wave are described in, for example, U.S.Patent Publication No. 2015/0162658, which application is also herebyincorporated by reference in its entirety.

Systems and methods described herein utilize a free-space feedconfiguration to illuminate a reflective surface. The reflective surfaceis populated with adjustable plasmonic resonant waveguides. Throughoutthe disclosure, for each disclosed embodiment that involves illuminatinga surface with a free-space reference wave to provide a reflectingoutgoing or transmitted wave having a specific field pattern, areciprocal embodiment is also contemplated that involves reflecting anincoming or received wave from the surface and then detecting thereflected wave according to the specific field pattern. More generally,antenna systems and methods described herein may be used to transmit andreceive via the same device (transceive), transmit only, receive only,or transmit via one device and receive via a separate but similardevice. For the sake of brevity, such devices and methods may bedescribed as only transmitting or only receiving with the understandingthat other combinations of receiving and/or transmitting arecontemplated.

The presently described systems and methods operate at higherfrequencies than many of the publications described above. Specifically,the systems and methods described herein operate in the infrared and/orvisible-frequency ranges. As used herein, near-infrared, infrared,visible, and near ultraviolet frequencies may be generally referred toas “optical” frequencies and wavelengths. When operational frequenciesare scaled up to optical frequencies, the sizes of the individualscattering elements and the spacings between adjacent scatteringelements are proportionally scaled down to preserve the subwavelength(e.g., metamaterial) aspect of the technology. The relevant lengthscales for operation at optical frequencies may be on the order ofmicrons or smaller. Generally, the feature sizes are smaller thantypical length scales for conventional printed circuit board (PCB)processes. Accordingly, many of the embodiments of the presentdisclosure may be manufactured using micro-lithographic and/ornano-lithographic processes, such as complementarymetal-oxide-semiconductor (CMOS) fabrication methods.

The present systems and methods utilize substantially differentstructures that many of the publications described above. Specifically,the systems and methods described herein relate to plasmonic interfacesof metals and dielectrics. Various applications of the optical surfacescattering antennas described herein include, but are not limited to,imaging via light detection and ranging (LiDAR), imaging via structuredillumination, free-space optical communication (e.g., single-beam andmultiple-input-multiple-output (MIMO) configurations), and pointing andtracking for free-space optical communications.

In various embodiments, a reconfigurable antenna aperture is populatedwith adjustable plasmonic resonant waveguides. A surface plasmon is anon-radiative electromagnetic wave that travels at the interface betweena material with a negative permittivity at optical frequencies (e.g., aplasmonic metal like gold, silver, platinum, aluminum, etc.) and amaterial with a positive permittivity at optical frequencies (e.g., adielectric). Thus, an adjustable plasmonic resonant waveguide may beembodied as a dielectric with an adjustable permittivity sandwichedbetween two metal rails.

It is appreciated that the permittivity of the dielectric at opticalfrequencies is correlated with a dielectric constant of the dielectric,which is also closely related to the refractive index of the dielectricat optical frequencies. Thus, modest changes in the refractive index ofthe dielectric of a high-Q plasmonic resonant waveguide result in asubstantial shift in the resonant wavelength(s) of the high-Q plasmonicresonant waveguide. The higher the Q factor, the greater the shift inresonance for a given change in the dielectric constant.

Assuming a fixed frequency of operation near the resonance of theplasmonic resonant waveguides, a scattered field from the antenna systemmay vary in phase and/or amplitude as a function of the adjusteddielectric values of the individual plasmonic resonant waveguides.Although the phase and amplitude are correlated through the Lorentzianresonance, the phase of the field over the aperture may be used forholographic and/or beam-forming designs. The systems and methodsdescribed below allow for considerable control without additionallyintroduced phase-shifters.

The index modulation range of tunable dielectric material (e.g., anelectrically-adjustable dielectric) is limited based on materialselection. An antenna aperture with an array of tunable radiating orscattering elements may have high-Q, low-loss, subwavelength plasmonicresonant waveguides.

In various embodiments, tunable plasmonic resonant waveguides forscattering and/or radiating are described herein that have a relativelyhigh-Q, are low-loss, and are sufficiently tunable to provide full ornear-full phase control. As a specific example, a surface may beconfigured with a plurality of adjustable plasmonic resonant waveguides.The inter-element spacing of the adjustable plasmonic resonantwaveguides may be less than, for example, an optical operatingwavelength within an operational bandwidth. The surface may include anoptically reflective surface to reflect optical electromagneticradiation within the operational bandwidth.

In one embodiment, a plasmonic resonant waveguide may include a firstmetal rail extending from the surface and a second metal rail extendingfrom the surface. The first and second metal rails may comprise one ormore combinations of metals that support surface plasmons, such assilver, gold, and/or aluminum. Other plasmonic metals, such as copper,titanium, and/or chromium, may be used in some instances. Anelectrically-adjustable dielectric may be disposed in a channel betweenthe first and second metal rails to form an adjustable plasmonicresonant waveguide. The adjustable plasmonic resonant waveguide can betuned or adjusted by varying a voltage applied to theelectrically-adjustable dielectric.

Each of the metal rails may have a length that is greater than a width.The length of each elongated rail may also be greater than a height towhich each metal rail extends from the surface. The width of eachelongated metal rail may less than, equal to, or greater than the heightdepending on the specific configuration. The elongated metal rails mayextend perpendicular to the surface or at an angle relative to thesurface. As per the subsequently described illustrations, the elongatedmetal rails may appear as walls or ridges running between two ends oredges of the surface. A first metal rail may be substantially parallelto a second metal rail and the electrically-adjustable dielectric may bedisposed within a channel defined by the first and second metal rails.

As previously described, each adjustable plasmonic resonant waveguidemay include first and second metal rails extending from the surface to aheight H. Each of the metal rails may have a width W and a length L,where the length L may be much greater than the height H and/or thewidth W. Each plasmonic resonant waveguide may be defined by twosubstantially parallel metal rails that are substantially parallel toone another and spaced apart by a channel width C. Anelectrically-adjustable dielectric may be disposed within the channel.In some embodiments, the electrically-adjustable dielectric may fill thechannel to the tops of the metal rails and in other embodiments theelectrically-adjustable dielectric may only partially fill the channel.

A variable voltage differential may be applied (e.g., via a controller)to the first and second metal rails of each of the adjustable plasmonicresonant waveguides. The dielectric constant of theelectrically-adjustable dielectric may be varied based on an appliedvoltage differential. Each voltage differential may correspond to adifferent dielectric constant and associated refractive index, and eachdielectric constant or refractive index may correspond to a uniquereflection phase of each individual adjustable plasmonic resonantwaveguide.

In various embodiments, the surface may comprise an optically reflectiveand electrically conductive surface, such as a metal surface. As aspecific example, the surface comprises a layer of copper separated fromthe metal rails by an insulating layer. In another example, elongatedpatches of copper may extend beneath one or more channels of eachadjustable plasmonic resonant waveguide. The optically reflectivesurface may be positioned beneath or embedded within a substrate. Thesubstrate may be optically transparent or absorb most of the energy atwavelengths within the operational bandwidth. In some embodiments, thesubstrate may be substantially covered with a reflective metal. Thematerial may depend on the operational bandwidth and/or other desiredproperties of reflectivity. Examples of suitable metals for variousoperational bandwidths include copper, silver, gold, nickel, iridium,aluminum, etc.

In some embodiments, reflective patches or reflective coatings on thesubstrate may be formed as high-reflective patches or coatings with morethan one layer of material (e.g., a first layer with a high index ofrefraction and a second layer with a low index of refraction). Forexample, the surface may comprise alternating layers of dielectricshaving high and low indices of refraction. Such a reflector may beconfigured as or referred to as a Bragg reflector.

As previously noted, the surface may comprise a substrate entirelycovered with a reflective material as a layer. In other embodiments, thesurface may comprise a substrate that includes the reflective materialas an embedded layer. In other embodiments, a patch of reflectivematerial with dimensions corresponding to the dimensions of anadjustable plasmonic resonant waveguide is positioned substantiallybeneath each of the adjustable plasmonic resonant waveguides. In someembodiments, a non-conductive layer (e.g., silicon dioxide) may separatethe reflective patch or layer (which may be electrically conductive)from the metal rails and the electrically-adjustable dielectric.

The arrangement of adjustable plasmonic resonant waveguides on thesurface may be described as a metasurface with each adjustable plasmonicresonant waveguide functioning as a metamaterial device withsub-wavelength proportions relative to the operational bandwidth.Accordingly, the inter-element spacing between adjacent adjustableplasmonic resonant waveguide is generally less than one wavelength of asmallest wavelength within the operational bandwidth (e.g.,three-quarters of a wavelength or one-half of a wavelength). In someembodiments, the inter-element spacing may be significantly less thanone-half wavelength (e.g., one-fifth, one-tenth, or even less).

The adjustable plasmonic resonant waveguides may be arranged in aone-dimensional array defined perpendicular to the length of each of theadjustable plasmonic resonant waveguides. As previously described, theadjustable plasmonic resonant waveguides may be elongated to extend fromone end or edge of the surface to another end or edge of the surface. Insome embodiments, the one-dimensional array of elongated adjustableplasmonic resonant waveguides may be formed on a surface without one orboth ends of each adjustable plasmonic resonant waveguide extending tothe edge of the surface. That is, the one-dimensional array ofadjustable plasmonic resonant waveguides may be positioned on a surfacehaving greater dimensions that the length of each adjustable plasmonicresonant waveguide and/or the total width of the array of adjustableplasmonic resonant waveguides.

In some embodiments, substantially elongated metal rails may be arrangedsubstantially parallel to one another with substantially uniform spacingand the electrically-adjustable dielectric may be disposed within eachof the channels defined by adjacent metal rails. In such an embodiment,many of the adjustable plasmonic resonant waveguides may share a metalrail with an adjacent adjustable plasmonic resonant waveguide.

The resonance of an adjustable plasmonic resonant waveguide may depend,at least in part, on the height, width, and/or length of the metalrails. Accordingly, one or more of the dimensions of the metal rails maybe selected to attain a target operational bandwidth, target resonancebandwidth, target Q factor for the adjustable plasmonic resonantwaveguide, and/or other target functionality.

To provide a specific example, an elongated metal rail may extend fromthe surface to a height of between approximately 300 and 1500nanometers. For example, the elongated metal rails may extend from thesurface to a height of 400 nanometers for an embodiment that includes anoperational wavelength of 905 nanometers. In another embodiment, theelongated metal rails may extend from the surface to a height of 600nanometers for an embodiment that includes an operational wavelength of905 nanometers. For an operational bandwidth that includes longerwavelengths (e.g., 1550 nanometers), the elongated metal rails mayextend from the surface to a height of approximately 700 or 1050nanometers for second or third order harmonic embodiments, respectively.In still other embodiments, walls elongated metal rails exceeding 1500nanometers may be used. The exact height of the elongated walls may beadapted for a particular frequency or frequency band and/or to attainvarious target resonant characteristics as discussed below.

Each of the elongated metal rails may have a width between approximately50 and 300 nanometers. As an example, each of the elongated metal railsmay have a width of approximately 150 nanometers. Each elongated metalrail may be spaced from adjacent elongated metal rail(s) by a channelspacing or channel width of between 100 and 200 nanometers. In variousembodiments, the spacing between elongated metal rails may be uniform,patterned, random, or pseudorandom.

As described herein, adjustable plasmonic resonant waveguides may sharemetal rails. Thus, the interelement spacing, or pitch, of the adjustableplasmonic resonant waveguides may be described as the distance betweenthe center of a channel of a first adjustable plasmonic resonantwaveguide and the center of a channel of a second adjustable plasmonicresonant waveguide. In embodiments in which the widths of the channelsand plasmonic metal rails are uniform, the interelement spacing or pitchmay be equal to the combined width of the channel and a single plasmonicmetal rail.

In the one example, adjustable plasmonic resonant waveguides at the endsof a row of adjustable plasmonic resonant waveguide (i.e., aone-dimensional array of adjustable plasmonic resonant waveguides) shareonly one elongated metal rail while all of the other adjustableplasmonic resonant waveguides share both elongated metal rails withadjacent adjustable plasmonic resonant waveguides on either side. Insuch an embodiment, 100 elongated metal rails arranged substantiallyparallel to one another may form 99 adjustable plasmonic resonantwaveguides in a one-dimensional array.

The height and width dimensions of each of the elongated metal rails maybe based on a target resonance and/or Q factor for a wavelength orwavelengths within the operational bandwidth. The total number ofadjustable plasmonic resonant waveguides and the length of the metalrails in each of the adjustable plasmonic resonant waveguides may beselected to attain a target reflection surface for the antenna device.

While the above-described embodiments contemplate a one-dimensionalarray of elongated metal rails on a surface, in some embodiments, theelongated walls may be arranged in any number of columns having anynumber of rows to form an M×N array of adjustable plasmonic resonantwaveguides. A control system may include a matrix of circuitry toselectively address each of the adjustable plasmonic resonant waveguidesto supply a voltage differential between paired elongated metal rails.In still other embodiments, the elongated metal rails may be arranged inconcentric rings or as concentric sides of a polygon. For example, theelongated metal rails may be curved, such that the concentric rings arecircular. Alternatively, the elongated metal rails may be straight andarranged as concentric sides of a polygon such as a hexagon, octagon, orthe like.

In some embodiments, the elongated metal rails may have substantiallyrectangular bases, but the sides may be flared in (or out) slightly.Defects in manufacturing or quantifiable or expected artifacts ofmanufacturing may result in metal rails and/or channels that are notperfectly rectangular without departing from the scope and functionalityof the presently described embodiments. For example, metal rails mayhave planar walls, bases, or tops, or alternatively they may be slightlyconvex or concave without deviating from the scope of the presentlydescribed embodiments.

In some embodiments, the base of each metal rail may be slightly largeror smaller than the top of each metal rail, such that each metal railmay be shaped like an elongated and truncated pyramid or an invertedelongated and truncated pyramid. Such variations in shape may, in someinstances, be a product of manufacturing or etching. For example, anattempt to create rectangular bases using chemical or physical etchingmay result in slightly malformed shapes with rounded edges and bases andtops that may not have the same area as bases.

Adjustable plasmonic resonant waveguides may be configured to have aresonance and a Q factor selected for a particular frequency band andbased on the electrically-adjustable dielectric disposed within thechannels. Each of the plurality of adjustable plasmonic resonantwaveguides may be configured to be “high-Q” with a Q factor betweenapproximately 5 and 100. For instance, each of the plurality ofadjustable plasmonic resonant waveguides may have a Q factor betweenapproximately 10 and 30. In one specific embodiment, each of theplurality of adjustable plasmonic resonant waveguide has a Q factor ofapproximately 20.

As previously described, the elongated metal rails may be spaced by achannel width corresponding to the fundamental harmonic mode of thefrequencies within an optical operating bandwidth. In such anembodiment, one antinode can be realized in the channel width. Theheight of the metal rails may correspond to the fundamental harmonicmode as well, such that the number of magnetic field antinodes withinthe channel is 1 multiplied by the number of magnetic field antinodesthat can be realized along the length of the channel.

Alternatively, the height of the metal rails may be selected tocorrespond to the second order harmonic mode, such that two magneticfield antinodes can be realized within the channel between the surfaceand the tops of the metal rails. In such an embodiment, the number ofmagnetic field antinodes that can be realized within a single adjustableplasmonic resonant waveguide is equal to 2 multiplied by the number ofmagnetic field antinodes that can be realized along the length of thechannel. With a wider channel that accommodates two magnetic fieldantinodes, the number of magnetic field antinodes that can be realizedwithin a single adjustable plasmonic resonant waveguide is equal to 4multiplied by the number of magnetic field antinodes that can berealized along the length of the channel. Thus, the total number ofmagnetic field antinodes that can be formed within theelectrically-adjustable dielectric between the two metal rails of eachadjustable plasmonic resonant waveguide is a function of (i) the channelwidth, (ii) the vertical height from the surface, and (iii) the lengthof the metal rails. Any combination of heights, channel widths, andlengths can be selected to attain fundamental, second order, third order. . . etc. harmonic modes in the given dimension.

In various embodiments, the phase of the reflected electromagneticradiation (e.g., optical radiation) is dependent on the refractive indexof the electrically-adjustable dielectric disposed between pairs ofmetal rails. The refractive index and associated permittivity anddielectric constant of the electrically-adjustable dielectric isdynamically selectable and adjustable based on a bias voltage applied toone or both metal rails to create a voltage difference across theelectrically-adjustable dielectric.

A controller may be used to selectively apply voltage differentials tothe individual or groups of adjustable plasmonic resonant waveguides inan array. A pattern of voltage differentials applied to an array ofadjustable plasmonic resonant waveguides corresponds to a pattern ofindices of refraction of the adjustable plasmonic resonant waveguides,which in turn corresponds to a pattern of reflection phases of theadjustable plasmonic resonant waveguides. Due to the subwavelengthspacing and element sizes of the adjustable plasmonic resonantwaveguides, a pattern of reflection phases of the adjustable plasmonicresonant waveguides corresponds to a specific reflection pattern ofincident optical radiation.

Thus, a set of patterns of applied voltage differentials corresponds toa set of reflection patterns of incident optical radiations. An appliedvoltage differential pattern can be determined for optical beamformingin both transmit and receive applications. A target beamform can beattained by applying a determinable pattern of voltage differentials tothe individual or groups of adjustable plasmonic resonant waveguides.

An example of a suitable electrically-adjustable dielectric is liquidcrystal. In one specific embodiment, a voltage differential can bevaried between a first (low) voltage and a second (higher) voltage tovary the index of refraction of the liquid crystal by approximately tenpercent. Another suitable electrically-adjustable dielectric for someapplications is an electro-optic polymer. Electro-optic (EO) polymermaterials exhibit a refractive index change based on second orderpolarizability, known as the Pockels effect, where the index modulationis proportional to the applied static or radio frequency electric field.These materials are typically small molecule organics doped into apolymer host, which results in excellent solution processability. Theindex modulation is given by

Δn=½n ³ r ₃₃ E   Equation 1

In Equation 1, n is the linear refractive index, E is the appliedelectric field and r₃₃ is the Pockels coefficient. Since the electricfield is limited by dielectric breakdown, the goal of syntheticchemistry and materials development is to increase the Pockelscoefficient. State-of-the-art materials have Pockels coefficients of˜150 pm/V, resulting in a performance of Δn/n of approximately 2%. Moreexotic and recently-developed chemistries have resulted inelectro-optical polymers which could potentially achieve indexmodulation as large as 6%. Since the effect is due to a nonlinearpolarizability, the response time of electro-optical polymers isextremely fast (several fs), resulting in device modulation speedsof >40 GHz. Due to their large nonlinear coefficients compared withelectro-optic crystalline materials, such as lithium niobate,electro-optical polymers may be used as modulators, enablinghigh-density photonic integrated circuits.

A number of companies have commercialized the synthesis ofelectro-optical materials and their integration into Mach-Zendermodulators, such as Lightwave Logic and Soluxra. As a result, manychallenges associated with electro-optical polymers have been addressed,such as thermal stability, long-term operation, and the efficient poling(orientation) of the nonlinear molecules along the electric fielddirection. As a result, electro-optical materials can be used as theelectrically-adjustable dielectric in some applications. In someapproaches, electro-optical polymers may be suitable for applicationswhere MHz and GHz rate switching may be desired, such as LiDARsingle-beam scanning and structured illumination, or free-space opticalcommunications with holograms that simultaneously perform beamformingand data encoding (thus allowing multi-user MIMO schemes).

As previously noted, liquid crystals may be used as anelectrically-adjustable dielectric. Liquid crystals are a wide class oforganic materials that exhibit anisotropy in the refractive index, whichdepends on molecular orientation and is controlled with an alternatingcurrent electric field. In the widely-used nematic liquid crystals,modulation between the extraordinary and ordinary refractive index canbe up to 13%, exceeding the performance of electro-optical polymers.However, because the index modulation occurs due to physicalreorientation of the entire molecule, the switching times in typicalliquid crystal devices such as displays are relatively slow (˜10millisecond), limited by the rotational viscosity and the elasticconstant of the liquid.

As compared to micro-scale displays, the switching time of liquidcrystals can be significantly reduced in geometries with smallerelectrode spacing and materials optimized for low viscosity, such thatmicrosecond switching times are possible in metasurface structures. Theswitching time is mostly limited by the on-to-off transition due toelastic relaxation, and consequently device geometries employingorthogonal electrodes can reduce the switching times even further.

The ubiquity of liquid crystal materials, their industrial production,and their robustness are major advantages of liquid crystals for usewith dynamic optical metasurfaces. In some approaches, a liquid crystalmaterial having a relatively low switching speed may be suitable toprovide dynamic holograms for free-space optical communications, wherethe optical beam may be steered on the time scale of transmitter andreceiver motion and vibration, typically on the millisecond timescale.In other approaches, a liquid crystal material having a relatively highswitching speed (e.g., as enhanced by the use of low viscosity liquidcrystals and/or counter-electrode geometries) may be suitable forscanning LiDAR and/or computational imaging based on structuredillumination where MHz speeds may be desired.

In still other embodiments, one or more types of chalcogenide glassesmay be used as the electrically-adjustable dielectric. Chalcogenideglasses have a unique structural phase transition from the crystallineto the amorphous phase—which have significantly different electrical andoptical properties—with index modulation in the shortwave infraredspectrum of over 30%.

The phase transition of chalcogenide glasses is thermally induced andmay be achieved through direct electrical heating of the chalcogenide.One example is Ge₂Sb₂Te₅ (GST), which becomes crystalline at ˜200° C.and can be switched back to the amorphous state with a melt-quenchingtemperature of ˜500 ° C. In addition to the large index modulationbetween these two states (˜30%), another attractive feature is that thematerial state is maintained in the absence of any additional electricalstimulus. For this reason, GST may be used in non-volatile electronicmemory and has also been demonstrated as a constituent of all-opticalmemory.

In some approaches, a chalcogenide glass material may be suitable forapplications where it is desired to only occasionally reconfigure themetasurface and yet provide good thermal stability and environmentalstability. For example, in free-space optical links, gradual drift ofthe transmitter or receiver may be compensated by low duty-cycle changesto the beam-pointing direction. At the same time, the large indexmodulation in these materials allows for the use of lower-Q resonators,simplifying design and easing fabrication tolerances.

The various metasurface architectures described herein may be fabricatedusing standard CMOS-compatible materials and processes. For example, ametal reflector may be made from various CMOS-compatible metals such asaluminum or copper, without sacrificing performance. In the embodimentsdescribed herein, the minimum feature size is about 100 nanometers, wellwithin the limits of deep UV lithography. For example, 40-nanometer nodetechnology is now a commodity process offered by many CMOS foundries,while custom foundry services offered by Intel operate at the14-nanometer node. Furthermore, several foundries have recently beenestablished that focus specifically on photonic-electronic integration,such as AIM Photonics.

As previously described, the feature sizes of the adjustable plasmonicresonant waveguides may be varied for an operational bandwidth thatincludes a portion of the visible light spectrum, the infrared spectrum,the near-infrared spectrum, the short-wavelength infrared spectrum, themedium-wavelength infrared spectrum, the long-wavelength infraredspectrum, the far infrared spectrum, and various telecommunicationswavelengths like microwaves and beyond. In some embodiments, an array ofadjustable plasmonic resonant waveguides may include a first set ofelements for a first frequency band and a second set of elements for asecond frequency band. One set or the other may be utilized depending onwhich frequency band is operational at a given time. In otherembodiments, both sets of elements may be used simultaneously. Multiplesets of elements may be used for multiple frequency bands.

A transmitter may transmit optical radiation to the reflective surface.The reflective surface may reflect the transmitted optical radiationaccording to a reflection pattern (e.g., beamformed) based on a voltagedifferential pattern applied to the array of adjustable plasmonicresonant waveguides. Similarly, incident beamformed optical radiationmay be received by the array of adjustable plasmonic resonant waveguidesbased on the applied voltage differential pattern. The receivedbeamformed optical radiation may be reflected to a receiver. In someembodiments, a first array of adjustable plasmonic resonant waveguidesmay be used for transmitting and a second array of adjustable plasmonicresonant waveguides may be used for receiving. In other embodiments, asingle array of adjustable plasmonic resonant waveguides may be sharedfor both receiving and transmitting.

The control functionality of the adjustable plasmonic resonantwaveguides may be similar to the control of other metamaterial devicesand metasurfaces. By controlling the phase (e.g., reflection phase) ofindividual subwavelength elements, beamforming can be accomplished.Controlling the individual elements may be accomplished by calculation,optimization, lookup tables, and/or trial and error. The disclosuresreferenced above and incorporated herein by reference provide somesuitable examples for controlling individual elements. Other approachesknown in the art may be utilized as well. In fact, many existingcomputing devices and infrastructures may be used in combination withthe presently described systems and methods.

Some of the infrastructure that can be used with embodiments disclosedherein is already available, such as general-purpose computers, computerprogramming tools and techniques, digital storage media, andcommunication links. Many of the systems, subsystems, modules,components, and the like that are described herein may be implemented ashardware, firmware, and/or software. Various systems, subsystems,modules, and components are described in terms of the function(s) theyperform because such a wide variety of possible implementations exist.For example, it is appreciated that many existing programming languages,hardware devices, frequency bands, circuits, software platforms,networking infrastructures, and/or data stores may be utilized alone orin combination to implement a specific control function.

It is also appreciated that two or more of the elements, devices,systems, subsystems, components, modules, etc. that are described hereinmay be combined as a single element, device, system, subsystem, module,or component. Moreover, many of the elements, devices, systems,subsystems, components, and modules may be duplicated or further dividedinto discrete elements, devices, systems, subsystems, components ormodules to perform subtasks of those described herein. Any of theembodiments described herein may be combined with any combination ofother embodiments described herein. The various permutations andcombinations of embodiments are contemplated to the extent that they donot contradict one another.

As used herein, a computing device, system, subsystem, module, orcontroller may include a processor, such as a microprocessor, amicrocontroller, logic circuitry, or the like. A processor may includeone or more special-purpose processing devices, such asapplication-specific integrated circuits (ASICs), programmable arraylogic (PAL), programmable logic array (PLA), a programmable logic device(PLD), field-programmable gate array (FPGA), or another customizableand/or programmable device. The computing device may also include amachine-readable storage device, such as non-volatile memory, staticRAM, dynamic RAM, ROM, CD-ROM, disk, tape, magnetic, optical, flashmemory, or another machine-readable storage medium. Various aspects ofcertain embodiments may be implemented or enhanced using hardware,software, firmware, or a combination thereof.

The components of some of the disclosed embodiments are described andillustrated in the figures herein. Many portions thereof could bearranged and designed in a wide variety of different configurations.Furthermore, the features, structures, and operations associated withone embodiment may be applied to or combined with the features,structures, or operations described in conjunction with anotherembodiment. In many instances, well-known structures, materials, oroperations are not shown or described in detail to avoid obscuringaspects of this disclosure. The right to add any described embodiment orfeature to any one of the figures and/or as a new figure is explicitlyreserved.

The embodiments of the systems and methods provided within thisdisclosure are not intended to limit the scope of the disclosure but aremerely representative of possible embodiments. In addition, the steps ofa method do not necessarily need to be executed in any specific order,or even sequentially, nor do the steps need to be executed only once. Aspreviously noted, descriptions and variations described in terms oftransmitters are equally applicable to receivers, and vice versa.

FIG. 1A illustrates a simplified embodiment of an optical surfacescattering antenna device 100 with a plurality of elongated, plasmonicmetal rails 150-164 (white rectangular prisms). Anelectrically-adjustable dielectric (shown in grey) is shown within thechannels between the elongated metal rails 150-164. An insulator 195insulates the elongated metal rails 150-164 from an underlying reflector190. In the illustrated embodiment, the insulator 195 and the reflector190 may constitute a surface from which the elongated metal rails 150extend. In the illustrated embodiment, the elongated metal rails 150-164are elongated from one end or edge of the surface 190 and 195 to theother. In alternative embodiments, the insulator 195 and/or reflector190 may extend further than the elongated metal rails 150-164.

FIG. 1B illustrates an example of single, subwavelength, adjustableplasmonic resonant waveguide 150 extending from a surface that includesan optical reflector 197 and an insulator 199. As illustrated, theadjustable plasmonic resonant waveguide 150 comprises a first elongatedmetal rail 140 that extends up to a height H from the insulator 199 witha defined width W and length L.

As described in conjunction with FIG. 1A, the elongated metal rail 140may extend between edges of the underlying surface and/or at least beseveral times longer than it is wide. A second opposing elongated metalrail 142 is substantially parallel to the first elongated metal rail140. The first and second metal rails 140 and 142 may comprise one ormore combinations of metals that support surface plasmons, such assilver, gold, and/or aluminum, and may thus be referred to as plasmonicmetal rails. Other plasmonic metals, such as copper, titanium, and/orchromium, may be used in some embodiments.

An electrically-adjustable (e.g., tunable) dielectric 145 is disposedwithin a channel between the first 140 and second 142 metal rails. Insome embodiments, the dielectric 145 may be disposed all around thefirst 140 and second 142 metal rails, but it is at least disposed withinthe channel between the first 140 and second 142 metal rails. In someembodiments, the insulator 199 may comprise silicon dioxide and theelectrically-adjustable dielectric 145 may comprise liquid crystal. Inother embodiments, the insulator 199 and the electrically-adjustabledielectric 145 may be the same material and/or even formed as a singlecomponent.

The width W and height H of the first 140 and second 142 metal rails maybe selected to attain a specific resonant frequency tuning. Furthermore,the spacing (i.e., width of the channel) between the first 140 andsecond 142 metal rails and the height H of each of the first 140 andsecond 142 metal rails may be selected to correspond to a fundamentalharmonic mode, a second order harmonic mode, etc. The dimensions can beselected to attain a target number of magnetic field antinodes betweenthe first 140 and second 142 metal rails across the width of the channeland along the height of the channel. Similar dimension selections may bemade with respect to the length of the first 140 and second 142 metalrails.

As previously described, the electric rails 140 and 142, the reflector197, the insulator 199 and/or the dielectric 145 may be formed as partof or in conjunction with chemical etching, bonding, micro-lithographicprocesses, nano-lithographic processes, CMOS lithography, PECVD,reactive ion etching, electron beam etching, sputtering, and/or thelike.

As previously noted, the electrically-adjustable dielectric 145 maycomprise liquid crystal. In other embodiments, theelectrically-adjustable dielectric 145 may comprise one or more of anelectro-optic polymer, liquid crystals, a chalcogenide glass, and/orsilicon. Each of these materials may have a static or quasi-static indexof refraction for an operational bandwidth (i.e., an optical operationalbandwidth). However, by applying a voltage to one or both of the first140 and second 142 metal rails, a voltage differential between the twometal rails 140 and 142 can subject the electrically-adjustabledielectric 145 to an electric field.

A material for the electrically-adjustable dielectric 145 may beselected based on a desired tuning mechanism, refractive indexmodulation (shown as a percentage below), and typical frequencyresponse. Example values of four general categories of material areshown below in Table 1. It is, however, appreciated that differentvalues may be attained based on the specific species or properties of agiven material.

Material Tuning Mechanism Typical Δn/n Typical Frequency Electro-OpticPolymers Pockels Effect ≈2-4%  >10 GHz Liquid Crystals TunableBirefringence ≈13% ≈100 Hz Chalcogenide Glasses Phase Change ≈30% ≈100MHz Silicon Thermo-Optic Effect ≈0.3%  ≈kHz-MHz

Many materials considerations and tradeoffs may be considered in theselection of the tunable material. One material parameter is therelative refractive index modulation (Δn/n), which is highly correlatedwith the achievable local phase shift of the element. Materials withlarger index modulations allow for larger phase shifts for a givenresonance Q factor. To achieve full phase modulation, the resonance Qfactor of the element may be Q>n/Δn. In general, there is a tradeoffbetween index modulation and response speed of the material. Materialswith the largest index modulation of ˜30%—such as liquidcrystals—typically have response rates on the order of ˜100 Hz, whileelectro-optic polymers, based on the Pockels effect, typically haveindex modulation of 6% or less, but with GHz response rates. At the sametime, the material should have low optical absorption at the operatingwavelength if phase holograms with high efficiency are desired.

FIG. 1C illustrates conceptual representations of the electric 115 andmagnetic 120 energy densities, respectively, within the adjustableplasmonic resonant waveguide of FIG. 1B with excitation of an opticalwavelength at a grazing incidence angle of approximately 70-80° relativeto normal with transverse magnetic (TM) polarization. Examples ofpossible wavelengths include, for example, optical wavelengths ofapproximately 905 nanometers or 1,550 nanometers. A wide variety ofspecific wavelengths and/or bands of wavelengths could be used withsimilar effect.

The interface of the metal rails with the electrically-adjustabledielectric allows for a plasmonic transmission of a non-radiativeelectromagnetic wave between the upper portion of each adjustableplasmonic resonant waveguide and the surface (specifically thereflector). The permittivity of the electrically-adjustable dielectriccan be dynamically modulated based on the voltage differential appliedto the metal rails on either side of the channel. As illustrated, underthe grazing incidence excitation, the electric field 115 and themagnetic field 120 are strongly localized in the electrically-adjustabledielectric 145 between the first 140 and second 142 metal rails.

FIG. 2A illustrates an alternative, simplified embodiment of an opticalsurface scattering antenna device 200 with a plurality of elongated,plasmonic metal rails 250-264 forming channels within which anelectrically-adjustable dielectric is disposed. The surface from whichthe elongated metal rails 250-264 extends includes an insulator 290within which a plurality of reflector patches 293 are embedded (only afew of which are labeled to avoid obscuring the drawing). In theillustrated embodiment, a single reflector patch 293 underlies eachchannel of the plurality of adjustable plasmonic resonant waveguides.The embedded reflector patches 293 may be elongated to run the length ofeach of the channels between the elongated metal rails 250-264. Thus,the reflector patches 293 may be elongated reflector patches having alength that corresponds to the length of the elongated metal rails250-264 and associated channels.

FIG. 2B illustrates an example of single, subwavelength, adjustableplasmonic resonant waveguide 250 extending from a surface that includesan elongated optical reflector patch 293 embedded within an insulator290. As illustrated, the adjustable plasmonic resonant waveguide 250comprises a first elongated metal rail 240 and a second opposingelongated metal rail 242 is substantially parallel to the firstelongated metal rail 240. The first and second metal rails 240 and 242may comprise one or more combinations of metals that support surfaceplasmons, such as silver, gold, and/or aluminum, copper, titanium,and/or chromium.

As in previously described embodiments, an electrically-adjustabledielectric 245 is disposed within a channel between the first 240 andsecond 242 metal rails. As previously noted, the electrically-adjustabledielectric 245 may comprise liquid crystal. In other embodiments, theelectrically-adjustable dielectric 245 may comprise one or more of anelectro-optic polymer, liquid crystals, a chalcogenide glass, and/orsilicon. In various embodiments, the embedded reflector patch 293 mayreflect optical electromagnetic radiation from the adjustable plasmonicresonant waveguide formed by the first 240 and second 242 metal railsand the electrically-adjustable dielectric disposed within the channelformed therebetween.

FIG. 2C illustrates conceptual representations of the electric 215 andmagnetic 220 energy densities, respectively, within the adjustableplasmonic resonant waveguide of FIG. 2B with excitation of an opticalwavelength at a grazing incidence angle of approximately 70-80° relativeto normal with transverse magnetic (TM) polarization. The interface ofthe metal rails with the electrically-adjustable dielectric allows for aplasmonic transmission of a non-radiative electromagnetic wave betweenthe upper portion of each adjustable plasmonic resonant waveguide andthe reflector patch. As previously described, the permittivity of theelectrically-adjustable dielectric can be dynamically modulated based onthe voltage differential applied to the metal rails on either side ofthe channel. The embedded reflector patch 293 beneath the channel mayaffect the electric and magnetic fields, as illustrated.

FIG. 3A illustrates another alternative, simplified embodiment of anoptical surface scattering antenna device 300 with a plurality ofelongated, plasmonic metal rails 350-364 forming channels within whichan electrically-adjustable dielectric is disposed. The surface fromwhich the elongated metal rails 350-364 extends includes an insulator390 and an underlying reflector layer 397. As illustrated, a notch 393is formed in the reflector layer 397 beneath each channel of the variousadjustable plasmonic resonant waveguides. Only some of the notches arelabeled to avoid obscuring the drawing. The notches 293 may extend thelength of the channels and a have a width corresponding to the width ofthe one or more channels. In the illustrated embodiment, each notch 293has a width substantially equal to the width of the channel above it. Inother embodiments, the width of each notch 293 may be slightly greaterthan or slightly less than the width of each channel.

FIG. 3B illustrates an example of single, subwavelength, adjustableplasmonic resonant waveguide 350 extending from a surface that includesan elongated notch 393 in reflector layer 397 separated from theelongated metal rails 340 and 342 by an insulator layer 390. As inprevious embodiments, the adjustable plasmonic resonant waveguide 350comprises a first elongated metal rail 340 and a second, parallelelongated metal rail 342.

In the illustrated embodiment, the notch 393 in the reflector layer 397has a width slightly greater than the width of the channel within whichthe electrically-adjustable dielectric 345 is disposed. The first andsecond metal rails 340 and 342 may comprise one or more combinations ofmetals that support surface plasmons, such as silver, gold, and/oraluminum, copper, titanium, and/or chromium. As in previously describedembodiments, an electrically-adjustable dielectric 345 is disposedwithin a channel between the first 340 and second 342 metal rails.

FIG. 3C illustrates conceptual representations of the electric 315 andmagnetic 320 energy densities, respectively, within the adjustableplasmonic resonant waveguide of FIG. 3B with excitation of an opticalwavelength at a grazing incidence angle of approximately 70-80° relativeto normal with transverse magnetic (TM) polarization. As previouslydescribed, the permittivity of the electrically-adjustable dielectriccan be dynamically modulated based on the voltage differential appliedto the metal rails on either side of the channel. The notch 393 withinthe underlying reflector layer 393 affects the electric and magneticfield densities as illustrated. The dielectric spacer (e.g., insulatorlayer 390) can be located at a node of the magnetic field in theplasmonic waveguide to minimize coupling between adjacent waveguides.

FIG. 4A illustrates another alternative embodiment of an optical surfacescattering antenna device 400 with a plurality of elongated, plasmonicmetal rails 450-464 forming channels within whichelectrically-adjustable dielectrics are disposed. The surface 490 fromwhich the elongated metal rails 450-464 extends includes alternatinglayers of dielectrics having low and high indices of refraction (shownas alternating layers of light and dark fill patterns). The alternatinglayers of dielectrics having low indices of refraction and dielectricshaving high indices of refraction create a Bragg reflector to reflectoptical wavelengths within the operational bandwidth of the antennadevice 400. In various embodiments, the number of layers may be adjusted(i.e., additional or fewer layers than illustrated) to attain a targetreflection efficiency.

FIG. 4B illustrates an example of single, subwavelength, adjustableplasmonic resonant waveguide 450 extending from a surface that includesmultiple layers of dielectrics. The layered dielectric surface providesa Bragg reflector to reflect optical wavelengths within the operationalbandwidth of the antenna and includes dielectrics having a relativelyhigh index of refraction 491, 493, and 495 that may or may not all havethe same index of refraction interleaved with dielectrics having arelatively low index of refraction 492, 494, and 496 that also may ormay not all have the same index of refraction. The number of layers mayvary and dots are shown to illustrate that the number of layers may bemuch greater than would fit in the illustration. As an example, in onespecific embodiment 17 layers are utilized.

As in previous embodiments, the adjustable plasmonic resonant waveguide450 comprises a first elongated metal rail 440 and a substantiallyparallel second elongated metal rail 442. An electrically-adjustabledielectric 445 is disposed within a channel therebetween. The first andsecond metal rails 440 and 442 may comprise one or more combinations ofmetals that support surface plasmons. An electrical contact may beconnected to each metal rail to selectively apply a voltage differentialthereto.

FIG. 4C illustrates conceptual representations of the electric 415 andmagnetic 420 energy densities, respectively, within the adjustableplasmonic resonant waveguide of FIG. 4B with excitation of an opticalwavelength at a grazing incidence angle of approximately 70-80° relativeto normal with transverse magnetic (TM) polarization. As previouslydescribed, the permittivity of the electrically-adjustable dielectriccan be dynamically modulated based on the voltage differential appliedto the metal rails on either side of the channel.

FIG. 5A illustrates an alternative, simplified embodiment of an opticalsurface scattering antenna device 500 with a plurality of elongated,plasmonic metal rails 550-564 forming channels within which anelectrically-adjustable dielectric is disposed. The surface from whichthe elongated metal rails 550-564 extends includes an insulator 590within which a plurality of reflector patches 593 are embedded. In theillustrated embodiment, a single, elongated reflector patch 593underlies every three channels of the various adjustable plasmonicresonant waveguides.

The embedded reflector patches 593 may be elongated to run the length ofeach of the channels between the elongated metal rails 550-564. FIG. 2Billustrates an embodiment in which the width of each embedded reflectorpatch corresponds to the width of a single channel. Alternativeembodiments may include embedded reflector patches that correspond toany number of channels. In some embodiments, the widths of eachreflector patch may be varied such that some reflector patches span asingle channel, others may span two or three channels, and still othersmay span even more channels.

FIG. 5B illustrates an example of three, subwavelength, adjustableplasmonic resonant waveguides 550 extending from a surface that includesan elongated optical reflector patch 593 embedded within an insulator590. The elongated optical reflector patch 593 has a width correspondingto the width of the three adjustable plasmonic resonant waveguides 550.Each of the adjustable plasmonic resonant waveguides 550 comprises anelectrically-adjustable dielectric 545, 547, and 551 disposed within achannel between two opposing metal rails 540, 542, 549, and 553.

FIG. 6 illustrates an approximation of the effective reflection phase ofa single adjustable plasmonic resonant waveguide as a function ofrefractive index of the electrically-adjustable dielectric. Asillustrated, the reflection phase of the adjustable plasmonic resonantwaveguide can be varied significantly based on the refractive index ofthe dielectric. As illustrated, a phase modulation of nearly 27 ispossible with a refractive index modulation of just 7%.

FIG. 7 illustrates an approximation of a reflection spectrum of a high-Qadjustable plasmonic resonant waveguide. This high sensitivity to therefractive index of the dielectric is enabled by the high-Q of theresonance (Q=64) in the illustrated example. The devices describedherein exhibit a high sensitivity of the reflection phase to therefractive index of the electrically-adjustable dielectric disposed inthe channel between the first and second metal rails. The highsensitivity and the ability to tune or adjust the refractive index ofthe dielectric facilitates the functionality of the dynamic metasurfacesdescribed herein.

In an illustrative embodiment, the high-Q dielectric resonances areutilized to define a one-dimensional beamforming hologram. The use of aone-dimensional hologram is for convenient illustration only, and otherembodiments provide a two-dimensional hologram. In one approach, thehologram phase may be calculated, for example, by using aGerchberg-Saxton algorithm, while imposing a phase-amplitude constraintin the plane of the hologram due to the Lorentzian resonant nature ofthe metasurface elements. The calculated phase at each dielectricresonant element is highly correlated with the refractive index of theadjustable refractive index of each dielectric resonant element.

By adjusting the refractive index, a pattern of refractive indices canbe attained that corresponds to a specific holograph phase. Therefractive index of each dielectric resonant element may be mapped to aspecific applied voltage differential. Accordingly, each pattern ofapplied voltage differentials corresponds to a unique pattern ofrefractive indices and a corresponding phase holograph.

FIG. 8 illustrates a simplified diagram of steerable beam 850 ofreflected optical radiation possible via an optical surface scatteringantenna 800 similar to the antenna illustrated in FIG. 1A. Asillustrated, an insulator layer 895 separates the plurality ofadjustable plasmonic resonant waveguides from the underlying reflector890.

FIG. 9 illustrates a simplified embodiment of an array 900 of 14adjustable plasmonic resonant waveguides on top of a surface 990including an insulator and a reflector. While this simplified array 900shows only 14 adjustable plasmonic resonant waveguides, functionalembodiments may include thousands, tens of thousands, hundreds ofthousands, or even millions of adjustable plasmonic resonant waveguidesin a one-dimensional array as illustrated or organized in various rowsand columns. For example, an antenna that is 3 centimeters wide mayinclude tens of thousands of adjustable plasmonic resonant waveguides(e.g., approximately 90,000 for 350-nanometer devices). Larger antennasmay include a proportionally larger number of adjustable plasmonicresonant waveguides depending on the feature sizes for a givenoperational bandwidth. In the illustrated embodiment, each of the metalrails 902-914 is shared by two adjustable plasmonic resonant waveguides,while the two end metal rails 901 and 915 are not shared.

Each of the metal rails 901-915 may be connected to an electrical leadto provide a specific voltage value and thereby induce a desiredelectric field within the electrically-adjustable dielectrics disposedwithin the channels formed between each pair of adjacent metal rails910-915. In some embodiments, the voltage values applied from one end tothe other are continuously increasing.

For example, assuming a voltage differential up to 1.5 volts is desiredbetween each adjacent set of metal rails, then for the illustratedembodiment that includes 15 metal rails 901-915, a voltage range from−10 volts at one end (metal rail 901) to +11 volts at the other end(metal rail 915) would be sufficient. In some embodiments, a 1.5 voltagedifferential may not provide a sufficient range of adjustability and ahigher voltage differential between adjacent metal rails may beutilized. In other embodiments, 1.5 volts may provide a greater rangethan needed and so a lower voltage differential may be employed. Inembodiments in which tens, thousands, or even tens of thousands ofmetals rails are employed, a voltage pattern may be repeated numeroustimes. For example, 10 metal rails may utilize a voltage rage from −5volts to +5 volts. Adjacent metal rails at the beginning and end of eachset of 10 metal rails may see a voltage differential of the full 10volts and may or may not function in the same manner as the otheradjustable plasmonic resonant waveguides that experience the “normal”voltage differentials. In embodiments in which liquid crystals are theelectrically adjustable material, a smaller voltage range may besufficient, since liquid crystals respond only to the magnitude of theelectric field.

As illustrated, the plurality of adjustable plasmonic resonantwaveguides 900 may constitute a holographic metasurface 950. Controllogic 952, memory 954, and an input/output port 956 may be paired withthe holographic metasurface 950 to form a transmit and/or receiveoptical surface scattering antenna system. In other embodiments, thecontrol electronics for the plasmonic waveguides may be located on aseparate chip and connected to the metasurface chip via wirebonds,wirelessly, or via other interconnect methods.

The control logic may provide voltage signals to each dielectric memberto create an electric field within the electrically-adjustabledielectric between each of the metal rails 901-915. A pattern of voltagedifferentials may be generated by the control logic to attain a specificpattern of refractive indices that corresponds to a target reflectionpattern of the optical surface scattering antenna system.

FIG. 10 illustrates a specific example of an adjustable plasmonicresonant waveguide 1000 configured to operate in a relatively narrowbandwidth that includes infrared light at 905 nanometers. In thespecific embodiment, the adjustable plasmonic resonant waveguide 1000includes two opposing metal rails 1040 and 1042 forming a channeltherebetween. An electrically-adjustable dielectric 1045 is disposedwithin the channel. The surface from which the adjustable plasmonicresonant waveguide 1000 extends includes an elongated reflector patch1093 embedded within an insulator 1090.

In the illustrated embodiment, the metal rails 1040 and 1042 may extendfrom the surface between approximately 400 and 600 nanometers dependingon the mode of operation (i.e., the number of magnetic field antinodesachievable along the height of the channel). The channel width may bebetween approximately 100 and 200 nanometers. The combined width of themetal rails 1040 and 1042 and the channel 1045 may be betweenapproximately 350 and 500 nanometers. One or both of the metal rails1040 and 1042 may be shared by an adjacent adjustable plasmonic resonantwaveguide so the effective pitch of the elements may be slightly lessthan the approximately 350- to 500-nanometer combined width.

The reflective patch 1093 may be embedded within the insulator 1090 by adepth of between 50 and 200 nanometers and may itself have a thicknessof between 50 and 500 nanometers. The width of the reflective patch 1093may be at least as wide as the channel or slightly wider than thechannel with a width of between approximately 200 and 500 nanometers.

FIG. 11A illustrates an example of a system 1100 that includes a tunableoptical surface scattering antenna device 1150 with an opticaltransmitter and/or receiver 1175 mounted to a base 1110. The opticaltransmitter and/or receiver 1175 may be configured to transmit opticalradiation to and/or receive optical radiation from the tunable opticalsurface scattering antenna device 1150 at a grazing angle of incidence(e.g., between 60 and 89 degrees). The tunable optical surfacescattering antenna device 1150 may be configured according to anycombination of embodiments described herein that employ adjustableplasmonic resonant waveguides extending from a surface that is orincludes a reflector.

For instance, the tunable optical surface scattering antenna device 1150may be configured with a plurality of elongated adjustable plasmonicresonant waveguides. The adjustable plasmonic resonant waveguides maycomprise a one-dimensional array of parallel, elongated metal rails withchannels formed therebetween. Electrically-adjustable dielectrics may bedisposed within the channels to provide a metal-dielectric interface thesupports plasmonic transmission at wavelengths within the operationalbandwidth.

FIG. 11B illustrates the transmitter 1175 (or receiver) transmitting (orreceiving) optical radiation 1180 at a grazing angle via a reflected,steerable optical beam 1185 from the tunable optical surface 1151 thatincludes elongated wall dielectric members. The beam 1185 may beadjusted in one direction as shown by the X-Z arrows. Electricalcontacts 1130 are illustrated to represent potential pinouts forapplying a voltage differential to each of the plurality of metal railswithin the tunable optical surface 1151. In some embodiments, many morepinouts may be available (as in FIG. 11A) and/or multiple metal railsmay be connected to the same pinout.

FIG. 12 illustrates an example embodiment of a packaged solid-statesteerable optical beam antenna system 1200 with an optically transparentwindow 1250. The illustrated embodiment may include a transmitter,receiver, and/or a transceiver within the package that are in opticalcommunication with one or more tunable optical surface scatteringantenna devices. For example, a transceiver may be paired with a singletunable optical surface scattering antenna device. Alternatively, thepackage may include a discrete transmitter and a discrete receiver thatare each in communication with their own tunable optical surfacescattering antenna device—one for receiving and one for transmitting.The package may protect the sensitive components and the opticallytransparent window 1250 may allow for a steerable beam to be steered atvarious angles.

This disclosure has been made with reference to various exemplaryembodiments, including the best mode. However, those skilled in the artwill recognize that changes and modifications may be made to theexemplary embodiments without departing from the scope of the presentdisclosure. While the principles of this disclosure have been shown invarious embodiments, many modifications of structure, arrangements,proportions, elements, materials, and components may be adapted for aspecific environment and/or operating requirements without departingfrom the principles and scope of this disclosure. These and otherchanges or modifications are intended to be included within the scope ofthe present disclosure.

This disclosure is to be regarded in an illustrative rather than arestrictive sense, and all such modifications are intended to beincluded within the scope thereof. Likewise, benefits, other advantages,and solutions to problems have been described above with regard tovarious embodiments. However, benefits, advantages, solutions toproblems, and any element(s) that may cause any benefit, advantage, orsolution to occur or become more pronounced are not to be construed as acritical, required, or essential feature or element. This disclosureshould, therefore, be determined to encompass at least the followingclaims.

What is claimed is:
 1. An apparatus, comprising: a surface; a pluralityof adjustable plasmonic resonant waveguides to convey plasmons thatextend from the surface and are arranged on the surface withinter-element spacings less than an optical operating wavelength of theapparatus.
 2. The apparatus of claim 1, wherein each of the plurality ofadjustable plasmonic resonant waveguides comprises anelectrically-adjustable dielectric and at least one plasmonic metalrail.
 3. The apparatus of claim 2, wherein each of the plurality ofadjustable plasmonic resonant waveguides comprises two plasmonic metalrails spaced from one another to form a channel therebetween, whereinthe electrically-adjustable dielectric is disposed within the channelbetween the two plasmonic metal rails.
 4. The apparatus of claim 1,wherein the surface comprises a dielectric substrate with an embeddedoptical reflector.
 5. The apparatus of claim 1, wherein the surfacecomprises a dielectric substrate with embedded optical reflectorsunderlying each of the adjustable plasmonic resonant waveguides.
 6. Theapparatus of claim 1, wherein the surface comprises a plurality ofoptically reflective patches.
 7. The apparatus of claim 1, wherein anoperational bandwidth includes a 905-nanometer wavelength and each ofthe adjustable plasmonic resonant waveguides extends from the surface toa height of approximately 400 nanometers.
 8. The apparatus of claim 1,wherein an operational bandwidth includes a 1550-nanometer wavelengthand each of the adjustable plasmonic resonant waveguides extends fromthe surface to a height of approximately 700 nanometers.
 9. Theapparatus of claim 3, wherein an operational bandwidth includes a905-nanometer wavelength, and wherein the two plasmonic metal rails ofeach of the adjustable plasmonic resonant waveguides are spaced from oneanother by a channel width of between approximately 100 and 200nanometers.
 10. The apparatus of claim 3, wherein an operationalbandwidth includes a 1550-nanometer wavelength, and wherein the twoplasmonic metal rails of each of the adjustable plasmonic resonantwaveguides are spaced from one another by a channel width of betweenapproximately 175 and 350 nanometers.
 11. The apparatus of claim 3,wherein the channel between the two plasmonic metal rails of each of theadjustable plasmonic resonant waveguides corresponds to a fundamentalharmonic mode of frequencies within an optical operating bandwidth. 12.The apparatus of claim 11, wherein each of the plasmonic metal railsextends from the surface to a height corresponding to the fundamentalharmonic mode of frequencies within the optical operating bandwidth. 13.The apparatus of claim 11, wherein each of the plasmonic metal railsextends from the surface to a height corresponding to a second orderharmonic mode of frequencies within the optical operating bandwidth,such that two magnetic field antinodes can be realized within thechannel between the surface and tops of the two plasmonic metal rails.14. The apparatus of claim 3, wherein the channel between the twoplasmonic metal rails of each of the adjustable plasmonic resonantwaveguides corresponds to a second order harmonic mode of frequencieswithin an optical operating bandwidth, such that two magnetic fieldantinodes can be realized within the electrically-adjustable dielectricbetween the two plasmonic metal rails.
 15. The apparatus of claim 14,wherein each of the plasmonic metal rails extends from the surface to aheight corresponding to a fundamental harmonic mode of frequencieswithin the optical operating bandwidth.
 16. The apparatus of claim 14,wherein each of the plasmonic metal rails extends from the surface to aheight corresponding to the second order harmonic mode of frequencieswithin the optical operating bandwidth, such that two magnetic fieldantinodes can be realized within the channel between the surface andtops of the plasmonic metal rails.
 17. The apparatus of claim 3, whereineach of the plasmonic metal rails of each of the adjustable plasmonicresonant waveguides extends from the surface to a height correspondingto a fundamental harmonic mode of frequencies within an opticaloperating bandwidth.
 18. A device, comprising: a converter to convertbetween electric power and optical electromagnetic radiation; a surfaceto reflect the optical electromagnetic radiation; a plurality ofadjustable plasmonic resonant waveguides arranged on the surface withinter-element spacings less than an optical operating wavelength of thedevice to convey plasmons and selectively apply a sub-wavelengthreflection phase pattern to the optical electromagnetic radiation. 19.The device of claim 18, further comprising a controller to selectivelyapply a pattern of voltages to the plurality of adjustable plasmonicresonant waveguides, wherein the converter illuminates the adjustableplasmonic resonant waveguides arranged on the surface with opticalelectromagnetic radiation, and wherein the pattern of voltagescorresponds to a pattern of reflection phases of the plurality ofadjustable plasmonic resonant waveguides to steer the reflected opticalelectromagnetic radiation.
 20. The device of claim 18, wherein each ofthe plurality of adjustable plasmonic resonant waveguides comprises: afirst plasmonic metal rail extending to a first height from the surface;a second plasmonic metal rail extending to a second height from thesurface, wherein the first and second plasmonic metal rails are spacedfrom one another to form a channel therebetween; and anelectrically-adjustable dielectric disposed within at least a portion ofthe channel.
 21. The device of claim 20, wherein each of the pluralityof adjustable plasmonic resonant waveguides further comprises:electrical contacts to receive an applied voltage differential to thefirst and second plasmonic metal rails, wherein application of a firstvoltage differential to the first and second plasmonic metal railcorresponds to a first reflection phase, and wherein application of asecond voltage differential to the first and second plasmonic metal railcorresponds to a second reflection phase.
 22. The device of claim 21,wherein the plurality of adjustable plasmonic resonant waveguides arearranged in a one-dimensional array perpendicular to a length of thefirst and second plasmonic metal rails.
 23. The device of claim 22,wherein each of the first and second plasmonic metal rails extendsbetween opposing edges of the surface.
 24. The device of claim 20,wherein the electrically-adjustable dielectric comprises a liquidcrystal material.
 25. The device of claim 20, wherein theelectrically-adjustable dielectric comprises an electro-optical polymermaterial.
 26. The device of claim 20, wherein theelectrically-adjustable dielectric comprises silicon.
 27. The device ofclaim 20, wherein the electrically-adjustable dielectric comprises achalcogenide glass.
 28. A method, comprising: conveying opticalelectromagnetic radiation to a reflective surface; and adjusting areflection phase for each of a plurality of adjustable plasmonicresonant waveguides to modify a reflection pattern of the conveyedoptical electromagnetic radiation, wherein the adjustable plasmonicresonant waveguides are configured to convey plasmons and are arrangedon the reflective surface with inter-element spacings less than anoptical operating frequency of the adjustable plasmonic resonantwaveguides.
 29. The method of claim 28, wherein the reflective surfacecomprises an optical reflector to reflect the conveyed opticalelectromagnetic radiation within an operational bandwidth that includesan optical operating wavelength.
 30. The method of claim 29, wherein theoptical reflector comprises an electrically conductive reflector. 31.The method of claim 30, wherein the electrically conductive reflectorcomprises a layer of metal.
 32. The method of claim 30, wherein each ofthe plurality of adjustable plasmonic resonant waveguides comprises anelectrically-adjustable dielectric and at least one plasmonic metalrail.
 33. The method of claim 32, wherein each of the plurality ofadjustable plasmonic resonant waveguides comprises two plasmonic metalrails spaced from one another to form a channel therebetween, whereinthe electrically-adjustable dielectric is disposed within the channelbetween the two plasmonic metal rails.
 34. The method of claim 33,further comprising: selectively applying, via a controller, a pattern ofvoltage differentials to the plasmonic metal rails of each of theplurality of adjustable plasmonic resonant waveguides, wherein thepattern of voltage differentials corresponds to (i) a pattern of indicesof refraction of the electrically-adjustable dielectric of each of theplurality of adjustable plasmonic resonant waveguides, and (ii) areflection pattern of a wave of optical electromagnetic radiationincident on the plurality of adjustable plasmonic resonant waveguides.35. A method, comprising: adjusting a reflection phase for each of aplurality of adjustable plasmonic resonant waveguides to conveyplasmons, wherein the adjustable plasmonic resonant waveguides arearranged on a reflective surface with inter-element spacings less thanan optical operating frequency of the adjustable plasmonic resonantwaveguides; and conveying optical electromagnetic radiation reflected bythe reflective surface to a receiver, wherein the opticalelectromagnetic radiation reflected by the reflective surface ismodified by a reflection pattern corresponding to the reflection phasesof each of the plurality of adjustable plasmonic resonant waveguides.36. The method of claim 35, further comprising: applying a pattern ofvoltages to the plurality of adjustable plasmonic resonant waveguides,wherein the pattern of voltages corresponds to a pattern of reflectionphases of the plurality of adjustable plasmonic resonant waveguides tosteer the reflected optical electromagnetic radiation.
 37. The method ofclaim 35, wherein the reflective surface comprises a Bragg reflectorcomprising alternating low and high index dielectric materials.
 38. Themethod of claim 35, wherein the plurality of adjustable plasmonicresonant waveguides are arranged in a one-dimensional array.